Guest Session: 1 Question Remaining. Create Account to save progress.
Login
Conditional Probabilityhard
0:00.0

Let X1,X2,…X_1, X_2, \dotsX1​,X2​,… be a sequence of independent Bernoulli random variables with parameter p∈(0,1)p \in (0, 1)p∈(0,1). Let T=inf⁡{n≥1:Xn=1,Xn+1=1}T = \inf \{n \geq 1 : X_n = 1, X_{n+1} = 1\}T=inf{n≥1:Xn​=1,Xn+1​=1} be the index of the first occurrence of two consecutive successes. What is the probability that T=3T = 3T=3?